Gaussian Pell Numbers

  • Authors

    • P. Balamurugan
    • A. Gnanam
    2018-10-02
    https://doi.org/10.14419/ijet.v7i4.10.26659
  • Pell sequence, Gaussian integers, Recurrence relations, Gaussian Pell number.

  • Gaussian numbers means representation as Complex numbers. In this work, Gaussian Pell numbers are defined from recurrence relation of Pell numbers. Here the recurrence relation on Gaussian Pell number is represented in two dimensional approach. This provides an extension of Pell numbers into the complex plane.

     

  • References

    1. [1] Harman CJ (1981) , Complex Fibonacci Numbers, The Fibonacci Quaterly, 13, 82-86.

      [2] Berzsenyi G (1975), Sums of Products of Generalized Fibonacci Numbers, The Fibonacci Quaterly, 13, 343-344.

      [3] Berzsenyi G (1977) , Gaussian Fibonacci Numbers, The Fibonacci Quaterly, 15 , 233-236.

      [4] A.F.Horadam AF (1961), A Generalized Fibonacci sequence, American Math. Monthly, 68, 455-459.

      [5] Horadam AF (1963), Complex Fibonacci Numbers and Fibonacci Quaternions, American Math. Monthly, 70, 289-291.

      [6] Lars. Ahlfors V (1979), Complex Analysis, Third Edition, Mcgraw-Hill Book Company .

      [7] Serge Lang (1977), Complex Analysis, Fourth Edition,Addison Wesley.

      [8] Ivan Niven, Herbert, Zukerman S & Huge Montgomery L(2004), An introduction to the theory of Numbers, Fifth Edition, John Wiley & Sons inc .

      [9] Hoggatt VE & Anaya JC (Feb.,1973), A Primer for the Fibonacci Numbers: Part XI,The Fibonacci Quarterly, Vol. 11, No.1 , pp. 85-90.

      [10] Sam Ganis E(1959), Notes on the Fibonacci sequence, this MONTHLY, Vol. 66, pp.129- 130.

      [11] Ivanoff VF (1959), Problem E 1347, this MONTHLY, vol. 66, pp. 592-593.

      [12] Dustan Everman, Danese AE & Venkannayah K (1960), Problem E 1396, this MONTHLY, vol.67, pp. 81-82.

      [13] Guest J (1960), A variant to Fibonacci’s sequence, Austral. Math. Teacher, vol.16, pp. 11- 15.

      [14] Dickson LE(1952) , History of the Theory of Numbers, vol. 1, New York, pp. 393-407. (For Tagiuri’s work, see p. 404.)

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  • How to Cite

    Balamurugan, P., & Gnanam, A. (2018). Gaussian Pell Numbers. International Journal of Engineering & Technology, 7(4.10), 1012-1014. https://doi.org/10.14419/ijet.v7i4.10.26659